Isotropic and anisotropic N-dimensional cosmologies with exponential potentials

We investigate (N + 1)-dimensional anisotropic cosmological models with a massless scalar held, self-interacting through an exponential potential. The problem is reduced to an FRW model with an additional free, massless scalar field. in the N not equal 1 case we find the exact general solution for the Robertson-Walker spacetime and the N > 3 anisotropic Bianchi type 1 model which is a product of a Bat (3 + 1)-dimensional manifold and an (N - 3)-dimensional torus. In both cases the solutions present singularities and power-law inflation. In the multidimensional anisotropic case we also analyse the conditions under which dimensional reduction can proceed. When N = 1 we consider the gravitational theory formed by setting the Ricci scalar equal to the trace of the energy-momentum tensor of the matter fields. In this case the exact general solution of the second-order system of gravitational and self-interacting scalar field equations exhibit singularities, their most notable departure from the N not equal 1 case being the absence of both particle horizons and power-law inflationary solutions.